Greg Kuperberg

Abstract

The notion of a completely saturated packing [Monats. Math. 125 (1998) 127-145] is
a sharper version of maximum density, and the analogous notion of a completely
reduced covering is a sharper version of minimum density. We define two
related notions: uniformly recurrent and weakly recurrent dense packings, and
diffusively dominant packings. Every compact domain in Euclidean space has a
uniformly recurrent dense packing. If the domain self-nests, such a packing is
limit-equivalent to a completely saturated one. Diffusive dominance is yet
sharper than complete saturation and leads to a better understanding of
n–saturation.